OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 7 — Mar. 1, 2012
  • pp: 823–833

Quantitative measurement of the orbital angular momentum density of light

Angela Dudley, Igor A. Litvin, and Andrew Forbes  »View Author Affiliations

Applied Optics, Vol. 51, Issue 7, pp. 823-833 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1122 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this work we derive expressions for the orbital angular momentum (OAM) density of light, for both symmetric and nonsymmetric optical fields, that allow a direct comparison between theory and experiment. We present a simple method for measuring the OAM density in optical fields and test the approach on superimposed nondiffracting higher-order Bessel beams. The measurement technique makes use of a single spatial light modulator and a Fourier transforming lens to measure the OAM spectrum of the optical field. Quantitative values for the OAM density as a function of the radial position in the optical field are obtained for both symmetric and nonsymmetric superpositions, illustrating good agreement with the theoretical prediction.

© 2012 Optical Society of America

OCIS Codes
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments
(090.1995) Holography : Digital holography
(070.3185) Fourier optics and signal processing : Invariant optical fields
(050.4865) Diffraction and gratings : Optical vortices
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:

Original Manuscript: September 23, 2011
Manuscript Accepted: November 15, 2011
Published: February 23, 2012

Angela Dudley, Igor A. Litvin, and Andrew Forbes, "Quantitative measurement of the orbital angular momentum density of light," Appl. Opt. 51, 823-833 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef]
  2. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995). [CrossRef]
  3. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001). [CrossRef]
  4. M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). [CrossRef]
  5. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000). [CrossRef]
  6. H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16, 9411–9416 (2008). [CrossRef]
  7. A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon three-dimensional quantum entanglement,” Phys. Rev. Lett. 89, 240401 (2002). [CrossRef]
  8. J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008). [CrossRef]
  9. J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010). [CrossRef]
  10. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004). [CrossRef]
  11. S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun. 175, 301–308 (2000). [CrossRef]
  12. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010). [CrossRef]
  13. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002). [CrossRef]
  14. M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014(2011). [CrossRef]
  15. C. Gao, X. Qi, Y. Liu, J. Xin, and L. Wang, “Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach–Zehnder interferometer and amplitude gratings,” Opt. Commun. 284, 48–51 (2011). [CrossRef]
  16. A. Gatto, M. Tacca, P. Martelli, P. Boffi, and M. Martinelli, “Free-space orbital angular momentum division multiplexing with Bessel beams,” J. Opt. 13, 064018 (2011). [CrossRef]
  17. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, “Angular Momentum,” Phys. Rev. Lett. 105, 053904 (2010). [CrossRef]
  18. V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003). [CrossRef]
  19. C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14, 6604–6612 (2006). [CrossRef]
  20. S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Residue orbital angular momentum in interferenced double vortex beams with unequal topological charges,” Opt. Express 14, 535–541 (2006). [CrossRef]
  21. K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt. 4, S82–S89 (2002). [CrossRef]
  22. V. Garces-Chavez, K. Volke-Sepulveda, S. Chavez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002). [CrossRef]
  23. M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Observation of the orbital angular momentum spectrum of a light beam,” Opt. Lett. 28, 2285–2287 (2003). [CrossRef]
  24. M. Hautakorpi, J. Lindberg, T. Setälä, and M. Kaivola, “Rotational frequency shifts in partially coherent optical fields,” J. Opt. Soc. Am. A 23, 1159–1163 (2006). [CrossRef]
  25. X. Gan, P. Zhang, S. Liu, Y. Zheng, J. Zhao, and Z. Chen, “Stabilization and breakup of optical vortices in presence of hybrid nonlinearity,” Opt. Express 17, 23130–23136 (2009). [CrossRef]
  26. I. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19, 16760–16771 (2011). [CrossRef]
  27. J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef]
  28. R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17, 23389–23395 (2009). [CrossRef]
  29. A. V. Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964). [CrossRef]
  30. D. W. K. Wong and G. Chen, “Redistribution of the zero order by the use of a phase checkerboard pattern in computer generated holograms,” Appl. Opt. 47, 602–610 (2008). [CrossRef]
  31. C. Lopez-Mariscal and K. Helmerson, “Shaped nondiffracting beams,” Opt. Lett. 35, 1215–1217 (2010). [CrossRef]
  32. A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, “Controlling the evolution of nondiffracting speckle by complex amplitude modulation on a phase-only spatial light modulator,” Opt. Commun. 285, 5–12 (2012). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited